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Math Help - Choosing K out of N Objects Formula Question

  1. #1
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    Choosing K out of N Objects Formula Question

    I'm having trouble interpreting the formula that is "with regard to order" and "without replacement". How exactly would I compute the upper right hand formula with, for example, k=5 and n=10?

    Choosing K out of N Objects Formula Question-test.png

    Sorry for the elementary question and thanks for your time.
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  2. #2
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    Re: Choosing K out of N Objects Formula Question

    Quote Originally Posted by divinelogos View Post
    I'm having trouble interpreting the formula that is "with regard to order" and "without replacement". How exactly would I compute the upper right hand formula with, for example, k=5 and n=10?
    You really should learn to post in LaTeX. It hard to know exactly what you are asking.
    Your table seems to be:
    \begin{array}{*{20}{c}}  {{n^k}}&{n(n - 1) \cdots (n - k + 1)} \\   {\binom{n-1+k}{k}}&{\binom{n}{k}} \end{array}
    Is that correct?

    If so the "upper right hand formula" is the permutation of N choosing k.
    i.e. _N\mathcal{P}_k=\frac{N!}{(N-k)!}.
    Thanks from divinelogos
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  3. #3
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    Re: Choosing K out of N Objects Formula Question

    I thought the picture would be clearer than Latex. But that seems to be correct! Thanks for the help
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